Angle-Angle-Side (AAS): If two angles and a non-included side of one triangle are congruent to two angles and the corresponding non-included side of a second triangle, then the two triangles are congruent.
Triangle ABC is congruent to triangle DEF by AAS congruency.
Interesting to Note:
In Elements, Euclid showed that for SAS, ASA,
AAS and SSS, if three corresponding parts of two triangles are congruent, then
all six parts have corresponding congruent parts. However, there are instances
in which five of the six parts of one triangle are congruent to five of the six
parts of another triangle without the triangles being congruent! Consider
the following pair of triangles. Five parts of one triangle are congruent to
five parts of the second triangle. But why are they not congruent?